Pith Number

pith:DFHA4RTV

pith:2017:DFHA4RTVYAI5KQCYVUTJDVUXHD

not attested not anchored not stored refs pending

Growth of higher Sobolev norms for energy critical NLS on irrational tori: small energy case

Yu Deng

arxiv:1702.05617 v1 · 2017-02-18 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DFHA4RTVYAI5KQCYVUTJDVUXHD}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:50:30.243652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

194e0e4675c011d54058ad2691d69738e971476bd7b0ca27b4aa9b9f2b18c4b6

Aliases

arxiv: 1702.05617 · arxiv_version: 1702.05617v1 · doi: 10.48550/arxiv.1702.05617 · pith_short_12: DFHA4RTVYAI5 · pith_short_16: DFHA4RTVYAI5KQCY · pith_short_8: DFHA4RTV

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DFHA4RTVYAI5KQCYVUTJDVUXHD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 194e0e4675c011d54058ad2691d69738e971476bd7b0ca27b4aa9b9f2b18c4b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a06331c8c926978e904e87627f7e262f2097da28ea29a5c073afcdfa403541e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-02-18T14:08:46Z",
    "title_canon_sha256": "361c466c9065d6a10adabc748c9b0315fa03c339b00926793d2285d4219d5e3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.05617",
    "kind": "arxiv",
    "version": 1
  }
}